How to use simulated annealing to optimize a simulation based, multicriteria Problem?

Hello all, I try to optimize some parameters of a Simulink Model which works fine. The outcome of this model are 3 values (energy used, elapsed time and the cost resulting) so this is a multicriteria problem. So far, for this use case, I have used the weighted sums method (all these criteria summed up) in conjunction with a patternsearch algorithm. There are 2 main questions resulting:

1. how can I optimize multicriteria using the simulated annealing algorithm? When I form a struct from the three output functions, simulannealbnd reports errors.

2. is there a possibility to tell the algorithm via constraints that not all values are allowed but that there is a certain step size (say lb=10 - ub=100 in steps of 10)?

Answer 1

[Alan Weiss]

Your question confuses me because you talk about having a multiobjective problem but then seem to want to use simulannealbnd to solve it. If you want to solve a multiobjective problem, use gamultiobj or paretosearch. See Multiobjective Optimization.

Alan Weiss

MATLAB mathematical toolbox documentation

[Robin]

Alright, that was my question behind it. So there is no way to have a simulated annealing algorithm solve a multiobjective problem!? (Atleast while using the optimization toolbox) Thanks for that answer!

My other question, though, is independent of that. Is there a possibility to limit the step size of the simulannealbnd via constraints or similar? E.g. that only multiples of 10 are possible and not the whole double is being searched through.

[Alan Weiss]

I didn't say there was no way. But it is ill-advised to use simulannealbnd for most purposes. It is a very slow solver, generally providing no benefit compared to patternsearch.

You can use a single-objective solver to find a Pareto front. See Generate and Plot Pareto Front for an example. That example uses fgoalattain, but you could use simulannealbnd as the scalar optimizer. You will have to extend the example from 2-D to 3-D, but that should not prove to be too difficult.

Bottom line: you CAN do it, but it seems to me to be a waste of time and resources. There are better ways.

Alan Weiss

MATLAB mathematical toolbox documentation

[Robin]

Your advice describes the method I currently use for simulated annealing. Then I will look at GA to determine if the multi-objective view is beneficial in my use case.

On the other point: I am currently optimizing (simulation based) the complete double range. After that i round the result to the points i want them to be (e.g. multiples of 10) and simulate again with those rounded numbers. Is this one of the ways youre reffering to?

Thanks for your answers!